TY - JOUR
T1 - On the Iterated Estimation of Dynamic Discrete Choice Games
AU - Bugni, Federico A.
AU - Bunting, Jackson
N1 - Publisher Copyright:
© 2020 The Author(s). Published by Oxford University Press on behalf of The Review of Economic Studies Limited.
PY - 2021/5/1
Y1 - 2021/5/1
N2 - We study the first-order asymptotic properties of a class of estimators of the structural parameters in dynamic discrete choice games. We consider K-stage policy iteration (PI) estimators, where K denotes the number of PIs employed in the estimation. This class nests several estimators proposed in the literature. By considering a "pseudo likelihood"criterion function, our estimator becomes the K-pseudo maximum likelihood (PML) estimator in Aguirregabiria and Mira (2002, 2007). By considering a "minimum distance"criterion function, it defines a new K-minimum distance (MD) estimator, which is an iterative version of the estimators in Pesendorfer and Schmidt-Dengler (2008) and Pakes et al. (2007). First, we establish that the K-PML estimator is consistent and asymptotically normal for any K ϵ ℕ. This complements findings in Aguirregabiria and Mira (2007), who focus on K=1 and K large enough to induce convergence of the estimator. Furthermore, we show under certain conditions that the asymptotic variance of the K-PML estimator can exhibit arbitrary patterns as a function of K. Second, we establish that the K-MD estimator is consistent and asymptotically normal for any K ϵ ℕ. For a specific weight matrix, the K-MD estimator has the same asymptotic distribution as the K-PML estimator. Our main result provides an optimal sequence of weight matrices for the K-MD estimator and shows that the optimally weighted K-MD estimator has an asymptotic distribution that is invariant to K. The invariance result is especially unexpected given the findings in Aguirregabiria and Mira (2007) for K-PML estimators. Our main result implies two new corollaries about the optimal 1-MD estimator (derived by Pesendorfer and Schmidt-Dengler (2008)). First, the optimal 1-MD estimator is efficient in the class of K-MD estimators for all K ϵ ℕ. In other words, additional PIs do not provide first-order efficiency gains relative to the optimal 1-MD estimator. Second, the optimal 1-MD estimator is more or equally efficient than any K-PML estimator for all K ϵ ℕ. Finally, the Appendix provides appropriate conditions under which the optimal 1-MD estimator is efficient among regular estimators.
AB - We study the first-order asymptotic properties of a class of estimators of the structural parameters in dynamic discrete choice games. We consider K-stage policy iteration (PI) estimators, where K denotes the number of PIs employed in the estimation. This class nests several estimators proposed in the literature. By considering a "pseudo likelihood"criterion function, our estimator becomes the K-pseudo maximum likelihood (PML) estimator in Aguirregabiria and Mira (2002, 2007). By considering a "minimum distance"criterion function, it defines a new K-minimum distance (MD) estimator, which is an iterative version of the estimators in Pesendorfer and Schmidt-Dengler (2008) and Pakes et al. (2007). First, we establish that the K-PML estimator is consistent and asymptotically normal for any K ϵ ℕ. This complements findings in Aguirregabiria and Mira (2007), who focus on K=1 and K large enough to induce convergence of the estimator. Furthermore, we show under certain conditions that the asymptotic variance of the K-PML estimator can exhibit arbitrary patterns as a function of K. Second, we establish that the K-MD estimator is consistent and asymptotically normal for any K ϵ ℕ. For a specific weight matrix, the K-MD estimator has the same asymptotic distribution as the K-PML estimator. Our main result provides an optimal sequence of weight matrices for the K-MD estimator and shows that the optimally weighted K-MD estimator has an asymptotic distribution that is invariant to K. The invariance result is especially unexpected given the findings in Aguirregabiria and Mira (2007) for K-PML estimators. Our main result implies two new corollaries about the optimal 1-MD estimator (derived by Pesendorfer and Schmidt-Dengler (2008)). First, the optimal 1-MD estimator is efficient in the class of K-MD estimators for all K ϵ ℕ. In other words, additional PIs do not provide first-order efficiency gains relative to the optimal 1-MD estimator. Second, the optimal 1-MD estimator is more or equally efficient than any K-PML estimator for all K ϵ ℕ. Finally, the Appendix provides appropriate conditions under which the optimal 1-MD estimator is efficient among regular estimators.
KW - Dynamic discrete choice problems
KW - Dynamic games
KW - Efficiency
KW - Estimation
KW - Minimum distance estimator
KW - Optimality
KW - Pseudo maximum likelihood estimator
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U2 - 10.1093/restud/rdaa032
DO - 10.1093/restud/rdaa032
M3 - Article
AN - SCOPUS:85113582793
SN - 0034-6527
VL - 88
SP - 1031
EP - 1073
JO - Review of Economic Studies
JF - Review of Economic Studies
IS - 3
ER -